Some new paranormed difference sequence spaces and weighted core

Fark Seri Uzayları ve Matris Dönüşümleri

“…To prove necessity and sufficiency of (15), let ∈ | | 1 (∇) be given and consider the operator (1) (∇) ∶ | | 1 (∇) → ℓ 1 defined by (3) with = 1. Further, ∈ | | 1 (∇) iff = (1) (∇)( ) ∈ ℓ 1 , and also by (5), let us consider the equality…”

“…Recently, there has been a lot of intrest in studies on the sequence spaces. In the literature, the basic concept is to generate new sequence spaces by means of the matrix domain of triangles (see, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]). Besides this, several authors have studied difference sequence spaces using some newly defined infinite matrices.…”

Some B-difference sequence spaces derived by generalized means and compact operators

“…II. if r n = 1 r ′ n , t n = s ′ n , s n = 1 ∀n, u = 1 and v = −1 then the sequence spaces X(r, s, t, p; B) reduce to X(r ′ , s ′ , p; ∆) for X ∈ {l ∞ (p), c(p), c 0 (p), l(p)} studied by Demiriz and Ç akan [8].…”

Applications of Orlicz–Pettis theorem in vector valued multiplier spaces of generalized weighted mean fractional difference operators

“…Altay and Basar [4] first studied generalized weighted mean operator G(p, q) which was further enlarged to a difference operator G(p, q, ) by Polat et al [26]. Later, Demiriz and Cakan [9] introduced generalized weighted mean of order m as G(p, q, m ). Consider a set of all sequences U and p = (p n ) such that p n = 0 ∀n ∈ N and 1 p = ( 1 p n…”